This paper presents a framework for the analysis of multi-antenna communication systems with mutually-coupled elements. The approach uses a network model that includes the coupled antennas, the propagation channel, the receiver matching network, a realistic noise model for the receive amplifiers, and externally generated interference. The general scheme is applied to diversity receivers, multiple-input multiple-output, and adaptive array architectures. Application of the formulation to coupled dipole antennas illustrates the impact of both mutual coupling and receiver matching on the performance of several representative multi-antenna applications.